{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "731f8427",
   "metadata": {},
   "source": [
    "## 蒙特卡罗"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "de25f450",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-10T01:18:38.498751Z",
     "start_time": "2024-05-10T01:18:36.373610Z"
    }
   },
   "outputs": [],
   "source": [
    "import gym\n",
    "import numpy as np\n",
    "from IPython import display\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "c6f4d893",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-10T01:19:19.482011Z",
     "start_time": "2024-05-10T01:19:19.464682Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((14, 3, False), {})"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "env=gym.make(\"Blackjack-v1\")\n",
    "env.reset()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "4f85d53a",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-10T01:18:20.837908Z",
     "start_time": "2024-05-10T01:18:20.832822Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(Tuple(Discrete(32), Discrete(11), Discrete(2)), Discrete(2))"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "env.observation_space,env.action_space"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "2a22856e",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-10T01:18:48.124841Z",
     "start_time": "2024-05-10T01:18:48.118339Z"
    }
   },
   "outputs": [],
   "source": [
    "class GymHelper:\n",
    "    def __init__(self,env,figsize=(3,3)):\n",
    "        self.env=env\n",
    "        self.figsize=figsize\n",
    "        plt.figure(figsize=figsize)\n",
    "        self.img=plt.imshow(env.render())\n",
    "    def render(self,title=None):\n",
    "        img_data=self.env.render()\n",
    "        self.img.set_data(img_data)\n",
    "        display.display(plt.gcf())\n",
    "        display.clear_output(wait=True)\n",
    "        if title:\n",
    "            plt.title(title)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "9847cd4e",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-10T01:19:23.132336Z",
     "start_time": "2024-05-10T01:19:22.213119Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 300x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "gym_helper=GymHelper(env)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "c02f42f4",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-10T01:21:30.070267Z",
     "start_time": "2024-05-10T01:21:30.065274Z"
    }
   },
   "outputs": [],
   "source": [
    "next_state,reward,terminated,truncated,info=env.step(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "02d6744d",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-10T01:21:41.948614Z",
     "start_time": "2024-05-10T01:21:41.943451Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((24, 3, False), -1.0, True, {})"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "next_state,reward,terminated,info"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "60b8c1ba",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-10T01:41:52.435895Z",
     "start_time": "2024-05-10T01:41:52.429911Z"
    }
   },
   "outputs": [],
   "source": [
    "Q={}\n",
    "explore_rate=0.2\n",
    "policy={}\n",
    "rewards={}\n",
    "num_episodes=5000\n",
    "alpha=0.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "0b5197a4",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-10T01:38:24.727254Z",
     "start_time": "2024-05-10T01:38:24.719763Z"
    }
   },
   "outputs": [],
   "source": [
    "#模拟回合\n",
    "def generate_episodes(Q,policy):\n",
    "    #回合观测序列表\n",
    "    episode=[]\n",
    "    #初始化环境状态\n",
    "    state,_=env.reset()\n",
    "    while True:\n",
    "        #如果第一次出现,将他添加到Q和policy中\n",
    "        if state not in Q.keys():\n",
    "            Q[state]={0:0,1:0}#初始化stick与hit的Q值\n",
    "            policy[state]=[0.5,0.5] #初始化stick与hit的概率,各为0.5\n",
    "            rewards[state]={0:[],1:[]} #初始化空列表用于储存累积奖励\n",
    "        #利用policy采样一个动作\n",
    "        action=np.random.choice([0,1],p=policy[state],size=1)[0]\n",
    "        #与环境交互,产生奖励与下一状态\n",
    "        next_state,reward,terminated,truncated,info=env.step(action)\n",
    "        #将状态,动作,奖励添加到epsisode中\n",
    "        episode.append((state,action,reward))\n",
    "        if terminated:\n",
    "            break\n",
    "        #更新状态\n",
    "        state=next_state\n",
    "    return episode"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "29ed1438",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-10T01:38:46.352700Z",
     "start_time": "2024-05-10T01:38:45.158425Z"
    }
   },
   "outputs": [],
   "source": [
    "for i in range(num_episodes):\n",
    "    #产生一个观测序列\n",
    "    episode=generate_episodes(Q,policy)\n",
    "    #初始化累积奖励\n",
    "    episode_sum_reward=0.0\n",
    "    #反向遍历观测序列中的每一步\n",
    "    for t in range(len(episode))[::-1]:\n",
    "        state,action,reward=episode[t]\n",
    "        #计算累积奖励\n",
    "        episode_sum_reward+=reward\n",
    "        rewards[state][action].append(episode_sum_reward)\n",
    "        #更新Q表中的Q值\n",
    "        Q[state][action]=np.mean(rewards[state][action])\n",
    "        #更新策略\n",
    "        policy_action=np.argmax(list(Q[state].values()))\n",
    "        policy[state][policy_action]=1-explore_rate\n",
    "        policy[state][1-policy_action]=explore_rate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "893c3667",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-10T01:41:01.663354Z",
     "start_time": "2024-05-10T01:41:01.124154Z"
    }
   },
   "outputs": [
    {
     "data": {
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       "  (13, 1, True): {0: 0.0, 1: -1.0},\n",
       "  (14, 1, True): {0: -1.0, 1: -1.0},\n",
       "  (20, 1, True): {0: 0.3333333333333333, 1: -1.0},\n",
       "  (17, 3, True): {0: -1.0, 1: 0.7142857142857143},\n",
       "  (19, 3, True): {0: -1.0, 1: 0.3333333333333333},\n",
       "  (20, 3, True): {0: 0.6, 1: 0.0},\n",
       "  (21, 4, True): {0: 1.0, 1: -0.3333333333333333},\n",
       "  (21, 6, False): {0: 0.9, 1: -1.0},\n",
       "  (17, 7, True): {0: -1.0, 1: 0.0},\n",
       "  (19, 1, True): {0: 0.5, 1: 0.0},\n",
       "  (16, 2, True): {0: -0.3333333333333333, 1: -0.3333333333333333},\n",
       "  (6, 5, False): {0: -0.2727272727272727, 1: -1.0},\n",
       "  (5, 1, False): {0: 0.0, 1: -0.5},\n",
       "  (20, 7, True): {0: 0.8, 1: 0.0},\n",
       "  (7, 6, False): {0: -0.2, 1: -0.6},\n",
       "  (15, 3, True): {0: -0.5, 1: -1.0},\n",
       "  (16, 3, True): {0: -1.0, 1: -1.0},\n",
       "  (14, 2, True): {0: -1.0, 1: 0.8},\n",
       "  (13, 9, True): {0: 0.0, 1: 0.3333333333333333},\n",
       "  (4, 3, False): {0: 0.0, 1: -1.0},\n",
       "  (16, 8, True): {0: -1.0, 1: 0.2},\n",
       "  (9, 7, False): {0: 0.0, 1: -0.75},\n",
       "  (9, 2, False): {0: -0.5, 1: 0.4166666666666667},\n",
       "  (13, 6, True): {0: 0.0, 1: 1.0},\n",
       "  (20, 2, True): {0: 0.6666666666666666, 1: 0.0},\n",
       "  (13, 5, True): {0: -1.0, 1: 0.3333333333333333},\n",
       "  (16, 5, True): {0: 0.0, 1: -1.0},\n",
       "  (5, 7, False): {0: 1.0, 1: 0.0},\n",
       "  (20, 8, True): {0: 0.5, 1: -0.3333333333333333},\n",
       "  (8, 4, False): {0: -1.0, 1: -0.25},\n",
       "  (21, 8, False): {0: 0.8888888888888888, 1: -1.0},\n",
       "  (5, 4, False): {0: 0, 1: -0.5},\n",
       "  (13, 7, True): {0: -0.3333333333333333, 1: -1.0},\n",
       "  (5, 8, False): {0: 0.0, 1: -1.0},\n",
       "  (6, 8, False): {0: 0.0, 1: 0.0},\n",
       "  (15, 2, True): {0: -0.3333333333333333, 1: 0.0},\n",
       "  (8, 3, False): {0: -0.6, 1: 0.2},\n",
       "  (4, 2, False): {0: -0.5, 1: -1.0},\n",
       "  (13, 3, True): {0: 0.3333333333333333, 1: 1.0},\n",
       "  (16, 9, True): {0: -1.0, 1: 1.0},\n",
       "  (14, 9, True): {0: -1.0, 1: -1.0},\n",
       "  (5, 5, False): {0: 0.0, 1: -1.0},\n",
       "  (14, 5, True): {0: 0.0, 1: -1.0},\n",
       "  (14, 6, True): {0: 0.3333333333333333, 1: -1.0},\n",
       "  (7, 3, False): {0: -0.5, 1: -1.0},\n",
       "  (19, 8, True): {0: 1.0, 1: -1.0},\n",
       "  (18, 3, True): {0: 0.42857142857142855, 1: 0},\n",
       "  (6, 9, False): {0: -0.3333333333333333, 1: -1.0},\n",
       "  (9, 9, False): {0: -0.3333333333333333, 1: -1.0},\n",
       "  (12, 2, True): {0: -1.0, 1: -1.0},\n",
       "  (5, 9, False): {0: -1.0, 1: -1.0},\n",
       "  (4, 4, False): {0: -1.0, 1: -1.0},\n",
       "  (12, 1, True): {0: -1.0, 1: 1.0},\n",
       "  (4, 9, False): {0: 1.0, 1: 0.0},\n",
       "  (18, 2, True): {0: 0.3333333333333333, 1: -0.3333333333333333},\n",
       "  (12, 3, True): {0: -1.0, 1: 0},\n",
       "  (18, 6, True): {0: -1.0, 1: 0.0},\n",
       "  (4, 7, False): {0: -1.0, 1: -1.0},\n",
       "  (5, 3, False): {0: 1.0, 1: 0.0},\n",
       "  (13, 2, True): {0: 1.0, 1: -1.0},\n",
       "  (5, 2, False): {0: 0.0, 1: 1.0},\n",
       "  (15, 6, True): {0: -1.0, 1: 0},\n",
       "  (14, 7, True): {0: -1.0, 1: 0},\n",
       "  (17, 5, True): {0: -0.3333333333333333, 1: 0}},\n",
       " {(16,\n",
       "   10,\n",
       "   False): {0: [-1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0], 1: [-1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0]},\n",
       "  (6, 7, False): {0: [1.0, 1.0, 1.0, -1.0, -1.0],\n",
       "   1: [1.0, -1.0, 1.0, 1.0, 1.0]},\n",
       "  (16,\n",
       "   7,\n",
       "   False): {0: [-1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0],\n",
       "   1: [-1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0]},\n",
       "  (15,\n",
       "   7,\n",
       "   False): {0: [1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0], 1: [1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0]},\n",
       "  (21, 7, False): {0: [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 0.0],\n",
       "   1: [-1.0, -1.0, -1.0]},\n",
       "  (10, 8, False): {0: [-1.0, -1.0, -1.0, -1.0],\n",
       "   1: [1.0, -1.0, -1.0, -1.0, -1.0, -1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0]},\n",
       "  (9, 8, False): {0: [-1.0, -1.0, -1.0, -1.0, -1.0, 1.0, -1.0],\n",
       "   1: [-1.0, 1.0, -1.0, -1.0, 1.0, 1.0, -1.0, 1.0, 1.0, 0.0, 0.0, 1.0, -1.0]},\n",
       "  (18,\n",
       "   8,\n",
       "   False): {0: [1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0], 1: [-1.0, -1.0, -1.0, -1.0, -1.0, -1.0]},\n",
       "  (16, 4, False): {0: [-1.0, -1.0, 1.0, 1.0, -1.0, -1.0, -1.0, -1.0, -1.0],\n",
       "   1: [1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0]},\n",
       "  (21, 4, False): {0: [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0],\n",
       "   1: [-1.0, -1.0, -1.0]},\n",
       "  (21,\n",
       "   9,\n",
       "   True): {0: [1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0], 1: [1.0, -1.0, -1.0, 1.0, -1.0, -1.0]},\n",
       "  (14,\n",
       "   7,\n",
       "   False): {0: [-1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0], 1: [-1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0]},\n",
       "  (18,\n",
       "   7,\n",
       "   False): {0: [-1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0], 1: [-1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0]},\n",
       "  (12,\n",
       "   10,\n",
       "   False): {0: [-1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0], 1: [-1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0]},\n",
       "  (17,\n",
       "   10,\n",
       "   False): {0: [1.0,\n",
       "    0.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0], 1: [-1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0]},\n",
       "  (15,\n",
       "   6,\n",
       "   False): {0: [1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0], 1: [-1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, 1.0]},\n",
       "  (20,\n",
       "   9,\n",
       "   False): {0: [1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0], 1: [-1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0]},\n",
       "  (18,\n",
       "   10,\n",
       "   False): {0: [-1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0], 1: [-1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0]},\n",
       "  (10, 2, False): {0: [-1.0, -1.0],\n",
       "   1: [-1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0]},\n",
       "  (20,\n",
       "   2,\n",
       "   False): {0: [1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0], 1: [-1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0]},\n",
       "  (20,\n",
       "   10,\n",
       "   False): {0: [0.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    0.0,\n",
       "    0.0,\n",
       "    0.0,\n",
       "    0.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    0.0,\n",
       "    0.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    0.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    0.0], 1: [-1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0]},\n",
       "  (21,\n",
       "   10,\n",
       "   False): {0: [1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0], 1: [-1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0]},\n",
       "  (21,\n",
       "   6,\n",
       "   True): {0: [1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0], 1: [1.0]},\n",
       "  (17, 4, True): {0: [-1.0, 1.0, 1.0, -1.0],\n",
       "   1: [-1.0, 1.0, 1.0, 1.0, 1.0, -1.0, 1.0, -1.0]},\n",
       "  (20,\n",
       "   7,\n",
       "   False): {0: [1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0], 1: [-1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0]},\n",
       "  (13,\n",
       "   1,\n",
       "   False): {0: [-1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0], 1: [-1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0]},\n",
       "  (20,\n",
       "   1,\n",
       "   False): {0: [0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0], 1: [-1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0]},\n",
       "  (15, 5, True): {0: [1.0, -1.0, -1.0, -1.0], 1: [-1.0]},\n",
       "  (19,\n",
       "   10,\n",
       "   False): {0: [1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0], 1: [-1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0]},\n",
       "  (17,\n",
       "   5,\n",
       "   False): {0: [1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0], 1: [1.0, 0.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0]},\n",
       "  (12, 2, False): {0: [1.0, 1.0, -1.0, 1.0, -1.0, -1.0, -1.0, 1.0, -1.0],\n",
       "   1: [1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0]},\n",
       "  (19,\n",
       "   2,\n",
       "   False): {0: [1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0], 1: [-1.0, -1.0, -1.0, -1.0]},\n",
       "  (10, 1, False): {0: [-1.0, -1.0, -1.0, -1.0, -1.0, 1.0, -1.0, -1.0, -1.0],\n",
       "   1: [-1.0, -1.0, 0.0, -1.0, -1.0]},\n",
       "  (11, 6, False): {0: [-1.0, -1.0, -1.0, 1.0, -1.0],\n",
       "   1: [0.0, -1.0, 1.0, 1.0, 0.0, -1.0, -1.0, 1.0, 1.0]},\n",
       "  (16,\n",
       "   6,\n",
       "   False): {0: [-1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0], 1: [0.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0]},\n",
       "  (19,\n",
       "   6,\n",
       "   False): {0: [0.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0], 1: [-1.0, -1.0, -1.0, -1.0, 1.0, -1.0, 1.0, -1.0, -1.0]},\n",
       "  (15,\n",
       "   10,\n",
       "   False): {0: [-1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0], 1: [-1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0]},\n",
       "  (21,\n",
       "   10,\n",
       "   True): {0: [1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0], 1: [1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    0.0,\n",
       "    -1.0]},\n",
       "  (11, 7, False): {0: [-1.0, -1.0],\n",
       "   1: [1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    -1.0]},\n",
       "  (12,\n",
       "   4,\n",
       "   False): {0: [-1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0], 1: [1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0]},\n",
       "  (19,\n",
       "   5,\n",
       "   False): {0: [1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0], 1: [-1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0]},\n",
       "  (18,\n",
       "   2,\n",
       "   False): {0: [1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0], 1: [-1.0, -1.0, -1.0, 1.0, -1.0, -1.0, -1.0]},\n",
       "  (19, 5, True): {0: [0.0, 1.0, 0.0], 1: [1.0, -1.0, 1.0, 1.0]},\n",
       "  (20,\n",
       "   6,\n",
       "   False): {0: [1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0], 1: [-1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0]},\n",
       "  (21,\n",
       "   8,\n",
       "   True): {0: [1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0], 1: [1.0, 1.0, -1.0, -1.0, 1.0, -1.0]},\n",
       "  (17,\n",
       "   1,\n",
       "   False): {0: [-1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0], 1: [-1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0]},\n",
       "  (15, 8, True): {0: [-1.0, -1.0, -1.0], 1: [1.0, 1.0, -1.0, 1.0, 1.0]},\n",
       "  (19, 4, True): {0: [1.0, 1.0, -1.0, 1.0, 1.0], 1: [1.0, -1.0]},\n",
       "  (12,\n",
       "   1,\n",
       "   False): {0: [-1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0], 1: [-1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0]},\n",
       "  (18, 1, True): {0: [0.0, -1.0, 1.0, -1.0], 1: [-1.0]},\n",
       "  (21,\n",
       "   1,\n",
       "   True): {0: [0.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    0.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0], 1: [-1.0, 1.0, 1.0, -1.0]},\n",
       "  (15,\n",
       "   1,\n",
       "   False): {0: [-1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0], 1: [-1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0]},\n",
       "  (11,\n",
       "   10,\n",
       "   False): {0: [-1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0], 1: [-1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0]},\n",
       "  (9,\n",
       "   10,\n",
       "   False): {0: [-1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0], 1: [-1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    1.0]},\n",
       "  (18,\n",
       "   9,\n",
       "   False): {0: [1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0], 1: [-1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0]},\n",
       "  (8,\n",
       "   10,\n",
       "   False): {0: [-1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0], 1: [1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0]},\n",
       "  (14,\n",
       "   2,\n",
       "   False): {0: [1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0], 1: [-1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    1.0]},\n",
       "  (15, 1, True): {0: [-1.0, -1.0], 1: [-1.0]},\n",
       "  (17, 1, True): {0: [-1.0, -1.0], 1: [-1.0]},\n",
       "  (15, 10, True): {0: [-1.0, 1.0, -1.0, -1.0, -1.0],\n",
       "   1: [-1.0, 0.0, 1.0, -1.0, -1.0, -1.0, 1.0, 1.0, -1.0, -1.0, -1.0]},\n",
       "  (14,\n",
       "   10,\n",
       "   False): {0: [-1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0], 1: [-1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0]},\n",
       "  (15,\n",
       "   8,\n",
       "   False): {0: [1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0], 1: [-1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0]},\n",
       "  (13,\n",
       "   3,\n",
       "   False): {0: [-1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0], 1: [-1.0, 1.0, -1.0, 0.0, 1.0, -1.0, -1.0, -1.0, -1.0, 1.0, -1.0]},\n",
       "  (14,\n",
       "   9,\n",
       "   False): {0: [-1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0], 1: [-1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0]},\n",
       "  (17,\n",
       "   4,\n",
       "   False): {0: [1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0], 1: [1.0, -1.0, -1.0, -1.0, -1.0, -1.0, 1.0, -1.0]},\n",
       "  (17, 9, True): {0: [-1.0, -1.0, -1.0, -1.0], 1: [-1.0]},\n",
       "  (14,\n",
       "   10,\n",
       "   True): {0: [-1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0], 1: [0.0, 0.0, -1.0, -1.0, 1.0, 0.0, -1.0, 1.0, -1.0, -1.0, -1.0, -1.0]},\n",
       "  (18,\n",
       "   10,\n",
       "   True): {0: [0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0], 1: [0.0, -1.0, -1.0, -1.0, -1.0, -1.0]},\n",
       "  (12,\n",
       "   9,\n",
       "   False): {0: [-1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0], 1: [-1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0]},\n",
       "  (14,\n",
       "   6,\n",
       "   False): {0: [-1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0], 1: [-1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0]},\n",
       "  (17,\n",
       "   8,\n",
       "   False): {0: [1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    0.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0], 1: [0.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0]},\n",
       "  (10, 6, False): {0: [-1.0, -1.0, 1.0],\n",
       "   1: [-1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0]},\n",
       "  (12,\n",
       "   6,\n",
       "   False): {0: [-1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0], 1: [-1.0, -1.0, -1.0, -1.0, -1.0, 1.0, -1.0]},\n",
       "  (11,\n",
       "   8,\n",
       "   False): {0: [1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0], 1: [0.0, -1.0, -1.0, 1.0, 0.0, 1.0]},\n",
       "  (20,\n",
       "   8,\n",
       "   False): {0: [0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0], 1: [-1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0]},\n",
       "  (21,\n",
       "   2,\n",
       "   True): {0: [1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0], 1: [1.0, 1.0, 1.0, 1.0, 1.0]},\n",
       "  (21,\n",
       "   2,\n",
       "   False): {0: [1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0], 1: [-1.0, -1.0, -1.0]},\n",
       "  (15,\n",
       "   9,\n",
       "   False): {0: [1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0], 1: [-1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0]},\n",
       "  (17,\n",
       "   9,\n",
       "   False): {0: [-1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    0.0], 1: [-1.0, -1.0, 0.0, -1.0, -1.0, -1.0, -1.0, -1.0, 1.0, -1.0]},\n",
       "  (11, 2, False): {0: [-1.0, -1.0, -1.0, -1.0, 1.0, 1.0, -1.0],\n",
       "   1: [1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0]},\n",
       "  (14, 4, True): {0: [-1.0, 1.0, -1.0, -1.0, 1.0, -1.0, -1.0], 1: [-1.0]},\n",
       "  (14,\n",
       "   4,\n",
       "   False): {0: [-1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0], 1: [1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0]},\n",
       "  (21, 3, True): {0: [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0],\n",
       "   1: [1.0, 1.0, 1.0, 1.0, -1.0, 1.0, -1.0, -1.0, -1.0, 1.0, -1.0]},\n",
       "  (20,\n",
       "   3,\n",
       "   False): {0: [1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    0.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0], 1: [-1.0, -1.0, 1.0, -1.0, -1.0, -1.0, -1.0, 1.0]},\n",
       "  (12, 5, True): {0: [-1.0], 1: [-1.0]},\n",
       "  (13,\n",
       "   10,\n",
       "   False): {0: [-1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0], 1: [-1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0]},\n",
       "  (11, 1, False): {0: [-1.0, -1.0, -1.0, -1.0, -1.0, 1.0],\n",
       "   1: [1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0]},\n",
       "  (21, 1, False): {0: [1.0, 1.0, 1.0, 0.0, 1.0, 1.0, 0.0, 1.0, 1.0, 0.0],\n",
       "   1: [-1.0]},\n",
       "  (13, 4, True): {0: [-1.0], 1: [1.0, -1.0, 1.0, 1.0]},\n",
       "  (16, 4, True): {0: [1.0, -1.0, -1.0, -1.0, 1.0, 1.0], 1: [-1.0, 1.0, -1.0]},\n",
       "  (10, 4, False): {0: [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, -1.0, -1.0],\n",
       "   1: [-1.0, -1.0]},\n",
       "  (18,\n",
       "   3,\n",
       "   False): {0: [-1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0], 1: [-1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0]},\n",
       "  (17, 2, True): {0: [-1.0, 1.0, 1.0], 1: [1.0, -1.0, -1.0, -1.0, 1.0]},\n",
       "  (17,\n",
       "   6,\n",
       "   False): {0: [1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    0.0,\n",
       "    0.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0], 1: [-1.0, 1.0, -1.0, 1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0]},\n",
       "  (18,\n",
       "   6,\n",
       "   False): {0: [-1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0], 1: [-1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0]},\n",
       "  (19,\n",
       "   4,\n",
       "   False): {0: [1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0], 1: [-1.0, -1.0, -1.0, -1.0, -1.0, 1.0, -1.0, -1.0, -1.0]},\n",
       "  (16,\n",
       "   8,\n",
       "   False): {0: [1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0], 1: [-1.0, -1.0, -1.0, -1.0, 1.0]},\n",
       "  (12, 3, False): {0: [-1.0, -1.0, 1.0, -1.0],\n",
       "   1: [1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0]},\n",
       "  (11, 3, False): {0: [1.0, 1.0, -1.0, -1.0, 1.0, 1.0, -1.0, -1.0, -1.0, 1.0],\n",
       "   1: [-1.0, 1.0, 1.0, -1.0, 1.0, 1.0, 1.0]},\n",
       "  (15,\n",
       "   3,\n",
       "   False): {0: [-1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0], 1: [-1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0]},\n",
       "  (15, 9, True): {0: [1.0, -1.0, 1.0, -1.0, -1.0, 1.0, 1.0], 1: [-1.0, 1.0]},\n",
       "  (12, 6, True): {0: [-1.0], 1: [-1.0, -1.0]},\n",
       "  (13,\n",
       "   4,\n",
       "   False): {0: [1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0], 1: [1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0]},\n",
       "  (12,\n",
       "   8,\n",
       "   False): {0: [1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0], 1: [-1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0]},\n",
       "  (10, 3, False): {0: [-1.0, 1.0, 1.0, 1.0, -1.0, -1.0, 1.0, 1.0, -1.0, 1.0],\n",
       "   1: [-1.0, 1.0, -1.0, -1.0, 0.0, 1.0, -1.0, 1.0, 1.0]},\n",
       "  (19,\n",
       "   7,\n",
       "   False): {0: [-1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0], 1: [1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0]},\n",
       "  (10,\n",
       "   7,\n",
       "   False): {0: [-1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0], 1: [-1.0, -1.0, 1.0]},\n",
       "  (19, 9, True): {0: [1.0, -1.0, 1.0, 1.0, 1.0, -1.0], 1: [0.0, 1.0]},\n",
       "  (20, 9, True): {0: [1.0, 1.0, 1.0, 0.0, -1.0, 1.0], 1: [0.0, -1.0, -1.0]},\n",
       "  (7,\n",
       "   9,\n",
       "   False): {0: [-1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0], 1: [-1.0, -1.0]},\n",
       "  (7, 4, False): {0: [-1.0, -1.0, -1.0, -1.0, 1.0, 1.0],\n",
       "   1: [-1.0, 0.0, -1.0, -1.0, 1.0, -1.0, -1.0, -1.0, -1.0, 0.0, -1.0]},\n",
       "  (4, 1, False): {0: [-1.0], 1: [-1.0]},\n",
       "  (12, 7, True): {0: [-1.0], 1: [1.0]},\n",
       "  (16,\n",
       "   5,\n",
       "   False): {0: [1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0], 1: [-1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0]},\n",
       "  (7, 1, False): {0: [-1.0, 1.0, -1.0, -1.0, 1.0, 1.0, -1.0, 1.0],\n",
       "   1: [-1.0, -1.0]},\n",
       "  (13, 10, True): {0: [-1.0, -1.0, 1.0, -1.0],\n",
       "   1: [1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    0.0]},\n",
       "  (17, 8, True): {0: [], 1: [1.0, 1.0, 0.0]},\n",
       "  (5, 6, False): {0: [1.0, 1.0, -1.0], 1: [-1.0, -1.0, -1.0]},\n",
       "  (20,\n",
       "   4,\n",
       "   False): {0: [1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    0.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    0.0], 1: [-1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0]},\n",
       "  (11,\n",
       "   4,\n",
       "   False): {0: [1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0], 1: [-1.0, -1.0, 1.0, -1.0]},\n",
       "  (13, 2, False): {0: [-1.0, -1.0, -1.0, -1.0, -1.0],\n",
       "   1: [1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0]},\n",
       "  (16, 1, True): {0: [], 1: [1.0, 1.0, 1.0, -1.0]},\n",
       "  (14,\n",
       "   1,\n",
       "   False): {0: [-1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0], 1: [1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0]},\n",
       "  (18,\n",
       "   1,\n",
       "   False): {0: [1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    0.0,\n",
       "    -1.0], 1: [-1.0, -1.0, -1.0, -1.0]},\n",
       "  (19,\n",
       "   8,\n",
       "   False): {0: [1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0], 1: [-1.0, 1.0, -1.0]},\n",
       "  (20, 4, True): {0: [1.0, 1.0, 1.0, 1.0, 1.0], 1: [-1.0]},\n",
       "  (18,\n",
       "   4,\n",
       "   False): {0: [-1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0], 1: [-1.0, -1.0, -1.0, -1.0, -1.0, -1.0]},\n",
       "  (14,\n",
       "   3,\n",
       "   False): {0: [-1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0], 1: [-1.0, -1.0, -1.0, -1.0, 1.0]},\n",
       "  (8, 9, False): {0: [-1.0, -1.0, -1.0, 1.0],\n",
       "   1: [1.0, -1.0, -1.0, 1.0, 1.0, -1.0, -1.0, 1.0]},\n",
       "  (17,\n",
       "   7,\n",
       "   False): {0: [0.0,\n",
       "    0.0,\n",
       "    0.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    0.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    0.0,\n",
       "    0.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0], 1: [1.0, 1.0, -1.0, -1.0, 1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0]},\n",
       "  (12,\n",
       "   5,\n",
       "   False): {0: [-1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0], 1: [-1.0, 0.0, -1.0, 1.0, -1.0, -1.0, -1.0, -1.0]},\n",
       "  (10,\n",
       "   10,\n",
       "   False): {0: [-1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0], 1: [1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0]},\n",
       "  (18, 8, True): {0: [-1.0, 0.0, 1.0, 0.0],\n",
       "   1: [1.0, 1.0, -1.0, 1.0, 1.0, 1.0]},\n",
       "  (18,\n",
       "   5,\n",
       "   False): {0: [0.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0],\n",
       "   1: [1.0, -1.0, -1.0, -1.0, 1.0, -1.0, -1.0, -1.0]},\n",
       "  (21, 5, False): {0: [1.0, 1.0, 1.0, 1.0, 1.0, 0.0, 1.0], 1: [-1.0]},\n",
       "  (19, 7, True): {0: [1.0, 1.0, 1.0, 1.0, 1.0, -1.0], 1: [1.0]},\n",
       "  (6,\n",
       "   10,\n",
       "   False): {0: [-1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0], 1: [-1.0, -1.0, -1.0, -1.0, -1.0, 1.0]},\n",
       "  (16,\n",
       "   3,\n",
       "   False): {0: [1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0], 1: [1.0, 0.0, -1.0, -1.0, -1.0, -1.0, 1.0]},\n",
       "  (16,\n",
       "   2,\n",
       "   False): {0: [1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0], 1: [-1.0, 1.0, -1.0, -1.0, -1.0, 0.0, -1.0, 1.0]},\n",
       "  (13, 8, False): {0: [-1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0],\n",
       "   1: [-1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0]},\n",
       "  (17,\n",
       "   10,\n",
       "   True): {0: [1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0], 1: [-1.0, -1.0, -1.0, 1.0]},\n",
       "  (17,\n",
       "   2,\n",
       "   False): {0: [1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    -1.0], 1: [-1.0, -1.0, -1.0, 1.0]},\n",
       "  (21,\n",
       "   5,\n",
       "   True): {0: [1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0], 1: [-1.0, 1.0, -1.0, -1.0]},\n",
       "  (15,\n",
       "   2,\n",
       "   False): {0: [-1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0], 1: [1.0, -1.0, -1.0, 1.0, -1.0, -1.0, -1.0, -1.0, 1.0, -1.0, -1.0, 1.0, -1.0, 1.0, 0.0, -1.0, 1.0, -1.0, -1.0, 1.0, -1.0, 1.0, -1.0, -1.0, -1.0, -1.0, -1.0]},\n",
       "  (14,\n",
       "   5,\n",
       "   False): {0: [1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0], 1: [1.0, -1.0, -1.0, -1.0, -1.0, 1.0, 1.0]},\n",
       "  (17, 6, True): {0: [-1.0, -1.0, -1.0, 1.0, 1.0, -1.0],\n",
       "   1: [-1.0, -1.0, -1.0]},\n",
       "  (14, 8, False): {0: [-1.0, -1.0, -1.0, 1.0, -1.0, -1.0, -1.0, -1.0],\n",
       "   1: [-1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0]},\n",
       "  (12,\n",
       "   7,\n",
       "   False): {0: [1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0], 1: [0.0, -1.0, -1.0, -1.0, -1.0, 1.0, -1.0]},\n",
       "  (19,\n",
       "   1,\n",
       "   False): {0: [1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    -1.0], 1: [-1.0, -1.0, -1.0, -1.0, -1.0, -1.0, 0.0, -1.0]},\n",
       "  (15, 7, True): {0: [-1.0], 1: [-1.0]},\n",
       "  (16, 7, True): {0: [-1.0, -1.0, 1.0, -1.0], 1: [-1.0]},\n",
       "  (21,\n",
       "   7,\n",
       "   True): {0: [1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0], 1: [-1.0]},\n",
       "  (9, 3, False): {0: [1.0, -1.0, -1.0, 1.0, 1.0, -1.0, 1.0, -1.0, 1.0, -1.0],\n",
       "   1: [-1.0, -1.0, -1.0, -1.0]},\n",
       "  (17,\n",
       "   3,\n",
       "   False): {0: [1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0], 1: [-1.0, -1.0, -1.0, 0.0, -1.0, -1.0]},\n",
       "  (8, 2, False): {0: [-1.0, -1.0, -1.0, -1.0, -1.0], 1: [-1.0, -1.0, -1.0]},\n",
       "  (9, 4, False): {0: [1.0, -1.0, -1.0, -1.0, 1.0, -1.0, 1.0, -1.0],\n",
       "   1: [-1.0, 1.0, -1.0, -1.0, 1.0, -1.0, -1.0]},\n",
       "  (8,\n",
       "   6,\n",
       "   False): {0: [-1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0], 1: []},\n",
       "  (5,\n",
       "   10,\n",
       "   False): {0: [-1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0], 1: [-1.0, -1.0]},\n",
       "  (13,\n",
       "   9,\n",
       "   False): {0: [-1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0], 1: [-1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0]},\n",
       "  (21,\n",
       "   3,\n",
       "   False): {0: [1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0], 1: [-1.0, -1.0]},\n",
       "  (7,\n",
       "   10,\n",
       "   False): {0: [1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0], 1: [-1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0]},\n",
       "  (19,\n",
       "   3,\n",
       "   False): {0: [1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0], 1: [-1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0]},\n",
       "  (19,\n",
       "   9,\n",
       "   False): {0: [-1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    0.0,\n",
       "    0.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0], 1: [-1.0, -1.0, -1.0]},\n",
       "  (16,\n",
       "   9,\n",
       "   False): {0: [-1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0], 1: [-1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0]},\n",
       "  (15,\n",
       "   4,\n",
       "   False): {0: [-1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0], 1: [-1.0, -1.0, -1.0, -1.0, 1.0, -1.0, -1.0, -1.0, -1.0, -1.0]},\n",
       "  (20, 5, True): {0: [1.0, 1.0, 1.0], 1: [-1.0]},\n",
       "  (20, 6, True): {0: [1.0, 1.0, 1.0, 1.0], 1: [1.0, -1.0, -1.0, 1.0]},\n",
       "  (7, 5, False): {0: [-1.0, -1.0, -1.0], 1: [-1.0, 0.0, -1.0, -1.0]},\n",
       "  (18, 5, True): {0: [0.0, 1.0, -1.0, 1.0], 1: [-1.0]},\n",
       "  (15, 4, True): {0: [-1.0, 1.0, 1.0, -1.0, 1.0], 1: [1.0, 1.0, -1.0]},\n",
       "  (18, 9, True): {0: [-1.0, 1.0], 1: [1.0, -1.0, 1.0, -1.0]},\n",
       "  (19, 10, True): {0: [-1.0, 1.0, 1.0, 1.0, -1.0, 1.0, -1.0],\n",
       "   1: [1.0, -1.0, 1.0, -1.0, 1.0, 1.0, -1.0, 1.0, 0.0, 1.0, 1.0]},\n",
       "  (16,\n",
       "   1,\n",
       "   False): {0: [-1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0], 1: [-1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0]},\n",
       "  (19, 2, True): {0: [0.0, 1.0, 1.0, -1.0, 1.0], 1: [-1.0, -1.0, -1.0]},\n",
       "  (7, 2, False): {0: [-1.0, -1.0, -1.0, -1.0],\n",
       "   1: [1.0, -1.0, -1.0, -1.0, 0.0, -1.0, 1.0, 1.0]},\n",
       "  (14, 8, True): {0: [1.0, -1.0, 1.0, -1.0], 1: [1.0, -1.0]},\n",
       "  (20,\n",
       "   5,\n",
       "   False): {0: [0.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0], 1: [-1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0]},\n",
       "  (13, 8, True): {0: [-1.0, -1.0, 1.0, -1.0, 1.0], 1: [-1.0]},\n",
       "  (20,\n",
       "   10,\n",
       "   True): {0: [1.0,\n",
       "    0.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    0.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    0.0], 1: [1.0, 0.0, -1.0, 1.0, -1.0, -1.0, -1.0, 1.0, -1.0, -1.0]},\n",
       "  (13,\n",
       "   7,\n",
       "   False): {0: [-1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0], 1: [-1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0]},\n",
       "  (4, 5, False): {0: [1.0, -1.0], 1: [1.0, -1.0]},\n",
       "  (9, 5, False): {0: [1.0, -1.0, -1.0, -1.0, -1.0, 1.0],\n",
       "   1: [1.0, 1.0, 0.0, -1.0, -1.0, -1.0, 1.0, -1.0, 0.0, 1.0]},\n",
       "  (9, 6, False): {0: [-1.0, 1.0, -1.0, -1.0, -1.0, 1.0, -1.0],\n",
       "   1: [-1.0, 1.0, -1.0, 1.0, 1.0, -1.0]},\n",
       "  (21, 9, False): {0: [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0],\n",
       "   1: [-1.0, -1.0, -1.0]},\n",
       "  (6, 2, False): {0: [-1.0, -1.0, 1.0], 1: [1.0, -1.0, -1.0, -1.0]},\n",
       "  (15,\n",
       "   5,\n",
       "   False): {0: [-1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0], 1: [-1.0, 1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0]},\n",
       "  (13,\n",
       "   6,\n",
       "   False): {0: [-1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0], 1: [-1.0, -1.0, -1.0, -1.0]},\n",
       "  (18, 7, True): {0: [1.0, 0.0, 0.0, 1.0, 1.0, -1.0], 1: []},\n",
       "  (12, 9, True): {0: [-1.0], 1: []},\n",
       "  (4, 8, False): {0: [-1.0], 1: []},\n",
       "  (8, 5, False): {0: [-1.0, -1.0, 1.0, 1.0, -1.0, -1.0, -1.0, 1.0, 1.0, -1.0],\n",
       "   1: [0.0, -1.0, -1.0, -1.0, 1.0, 1.0]},\n",
       "  (7, 7, False): {0: [-1.0, -1.0], 1: [-1.0, 1.0, -1.0, 0.0]},\n",
       "  (12, 10, True): {0: [-1.0, -1.0, 1.0], 1: [-1.0, 1.0, -1.0]},\n",
       "  (6, 1, False): {0: [-1.0, -1.0, 1.0], 1: [-1.0, -1.0, 1.0]},\n",
       "  (9, 1, False): {0: [-1.0, -1.0, -1.0, -1.0, -1.0],\n",
       "   1: [-1.0,\n",
       "    0.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    0.0]},\n",
       "  (10, 5, False): {0: [-1.0, -1.0, 1.0, -1.0, 1.0, -1.0, 1.0],\n",
       "   1: [-1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0]},\n",
       "  (8, 1, False): {0: [-1.0, -1.0, -1.0, 1.0, -1.0], 1: [-1.0, -1.0]},\n",
       "  (7, 8, False): {0: [-1.0],\n",
       "   1: [-1.0, 0.0, -1.0, -1.0, -1.0, 1.0, -1.0, -1.0, -1.0]},\n",
       "  (13, 5, False): {0: [-1.0, -1.0, 1.0, -1.0],\n",
       "   1: [-1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0]},\n",
       "  (10,\n",
       "   9,\n",
       "   False): {0: [-1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0], 1: [-1.0, -1.0, 1.0, -1.0]},\n",
       "  (8, 8, False): {0: [1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0],\n",
       "   1: [-1.0, -1.0, -1.0, -1.0, 1.0, -1.0]},\n",
       "  (4, 10, False): {0: [1.0, -1.0, -1.0, 1.0, 1.0, -1.0, 1.0], 1: [-1.0, -1.0]},\n",
       "  (11, 5, False): {0: [1.0, -1.0, -1.0, 1.0, -1.0, -1.0, -1.0],\n",
       "   1: [1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0]},\n",
       "  (11, 9, False): {0: [-1.0, -1.0],\n",
       "   1: [1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    0.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    0.0,\n",
       "    1.0,\n",
       "    1.0]},\n",
       "  (6, 3, False): {0: [-1.0, -1.0, -1.0, 1.0, -1.0],\n",
       "   1: [-1.0, -1.0, -1.0, -1.0, 1.0]},\n",
       "  (16, 6, True): {0: [1.0], 1: [-1.0, 1.0]},\n",
       "  (6, 4, False): {0: [-1.0, 1.0, -1.0],\n",
       "   1: [1.0, -1.0, -1.0, 1.0, 1.0, 1.0, -1.0, -1.0, -1.0]},\n",
       "  (6, 6, False): {0: [-1.0, 1.0, 1.0], 1: [0.0]},\n",
       "  (19, 6, True): {0: [-1.0, 1.0, 1.0, 1.0], 1: [-1.0, 1.0]},\n",
       "  (4, 6, False): {0: [1.0, -1.0], 1: [1.0]},\n",
       "  (14, 3, True): {0: [-1.0, 1.0], 1: [-1.0]},\n",
       "  (16, 10, True): {0: [-1.0, -1.0, -1.0],\n",
       "   1: [-1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0]},\n",
       "  (8, 7, False): {0: [1.0, 1.0, -1.0, -1.0, 1.0, -1.0],\n",
       "   1: [1.0, 1.0, 1.0, -1.0, 1.0, -1.0, -1.0, 0.0, -1.0]},\n",
       "  (18, 4, True): {0: [0.0, 0.0, 1.0, 1.0, -1.0, 1.0], 1: []},\n",
       "  (13, 1, True): {0: [-1.0, 1.0], 1: [-1.0]},\n",
       "  (14, 1, True): {0: [-1.0, -1.0, -1.0], 1: [-1.0, -1.0]},\n",
       "  (20, 1, True): {0: [-1.0, 1.0, 1.0], 1: [-1.0]},\n",
       "  (17, 3, True): {0: [-1.0], 1: [1.0, 1.0, 1.0, -1.0, 1.0, 1.0, 1.0]},\n",
       "  (19, 3, True): {0: [-1.0], 1: [1.0, 1.0, -1.0]},\n",
       "  (20, 3, True): {0: [1.0, 1.0, -1.0, 1.0, 1.0], 1: [1.0, -1.0]},\n",
       "  (21, 4, True): {0: [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0],\n",
       "   1: [1.0, -1.0, -1.0]},\n",
       "  (21, 6, False): {0: [1.0, 1.0, 1.0, 0.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0],\n",
       "   1: [-1.0]},\n",
       "  (17, 7, True): {0: [-1.0, -1.0], 1: [-1.0, 1.0]},\n",
       "  (19, 1, True): {0: [0.0, 1.0], 1: [0.0, 0.0]},\n",
       "  (16, 2, True): {0: [-1.0, -1.0, 1.0], 1: [-1.0, 1.0, -1.0]},\n",
       "  (6,\n",
       "   5,\n",
       "   False): {0: [1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0], 1: [-1.0]},\n",
       "  (5, 1, False): {0: [-1.0, 1.0], 1: [-1.0, -1.0, 1.0, -1.0]},\n",
       "  (20, 7, True): {0: [1.0, 0.0, 1.0, 1.0, 1.0], 1: [-1.0, 1.0]},\n",
       "  (7, 6, False): {0: [-1.0, -1.0, 1.0, 1.0, -1.0],\n",
       "   1: [1.0, -1.0, -1.0, -1.0, -1.0]},\n",
       "  (15, 3, True): {0: [-1.0, 1.0, -1.0, -1.0], 1: [-1.0]},\n",
       "  (16, 3, True): {0: [-1.0, -1.0, -1.0], 1: [-1.0]},\n",
       "  (14, 2, True): {0: [-1.0], 1: [0.0, 1.0, 1.0, 1.0, 1.0]},\n",
       "  (13, 9, True): {0: [1.0, 1.0, 1.0, 1.0, -1.0, -1.0, -1.0, -1.0],\n",
       "   1: [-1.0, 1.0, 1.0]},\n",
       "  (4, 3, False): {0: [-1.0, 1.0], 1: [-1.0]},\n",
       "  (16, 8, True): {0: [-1.0], 1: [1.0, -1.0, 1.0, 1.0, -1.0]},\n",
       "  (9,\n",
       "   7,\n",
       "   False): {0: [1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    1.0,\n",
       "    -1.0,\n",
       "    -1.0,\n",
       "    -1.0], 1: [-1.0, -1.0, -1.0, 0.0]},\n",
       "  (9, 2, False): {0: [-1.0, -1.0, 1.0, -1.0],\n",
       "   1: [0.0, -1.0, 1.0, 1.0, 1.0, 0.0, 1.0, 1.0, 0.0, 1.0, 1.0, -1.0]},\n",
       "  (13, 6, True): {0: [-1.0, 1.0], 1: [1.0]},\n",
       "  (20, 2, True): {0: [1.0, 0.0, 1.0], 1: [0.0, -1.0, 1.0]},\n",
       "  (13, 5, True): {0: [-1.0], 1: [1.0, 1.0, -1.0]},\n",
       "  (16, 5, True): {0: [1.0, -1.0], 1: [-1.0, -1.0]},\n",
       "  (5, 7, False): {0: [1.0], 1: [-1.0, 1.0]},\n",
       "  (20, 8, True): {0: [1.0, 1.0, -1.0, -1.0, 1.0, 1.0, 0.0, 1.0, 1.0, 1.0],\n",
       "   1: [-1.0, -1.0, 1.0]},\n",
       "  (8, 4, False): {0: [-1.0, -1.0, -1.0, -1.0],\n",
       "   1: [1.0, 1.0, 1.0, -1.0, -1.0, -1.0, -1.0, -1.0]},\n",
       "  (21, 8, False): {0: [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 0.0, 1.0],\n",
       "   1: [-1.0]},\n",
       "  (5, 4, False): {0: [], 1: [1.0, -1.0, -1.0, -1.0]},\n",
       "  (13, 7, True): {0: [-1.0, -1.0, 1.0], 1: [-1.0, -1.0]},\n",
       "  (5, 8, False): {0: [-1.0, 1.0, -1.0, 1.0], 1: [-1.0]},\n",
       "  (6, 8, False): {0: [1.0, 1.0, -1.0, -1.0], 1: [-1.0, 1.0]},\n",
       "  (15, 2, True): {0: [1.0, -1.0, -1.0], 1: [1.0, -1.0, 1.0, -1.0]},\n",
       "  (8,\n",
       "   3,\n",
       "   False): {0: [-1.0, -1.0, -1.0, -1.0, -1.0, 1.0, -1.0, 1.0, -1.0, -1.0],\n",
       "   1: [-1.0, -1.0, 1.0, 1.0, 1.0]},\n",
       "  (4, 2, False): {0: [-1.0, -1.0, -1.0, 1.0], 1: [-1.0]},\n",
       "  (13, 3, True): {0: [1.0, 1.0, -1.0], 1: [1.0]},\n",
       "  (16, 9, True): {0: [-1.0], 1: [1.0]},\n",
       "  (14, 9, True): {0: [-1.0, -1.0, -1.0], 1: [-1.0]},\n",
       "  (5, 5, False): {0: [1.0, -1.0, -1.0, 1.0], 1: [-1.0]},\n",
       "  (14, 5, True): {0: [-1.0, 1.0, 1.0, -1.0, -1.0, 1.0], 1: [-1.0]},\n",
       "  (14, 6, True): {0: [1.0, -1.0, 1.0], 1: [-1.0]},\n",
       "  (7, 3, False): {0: [-1.0, 1.0, -1.0, 1.0, -1.0, -1.0, -1.0, -1.0],\n",
       "   1: [-1.0]},\n",
       "  (19, 8, True): {0: [1.0, 1.0, 1.0, 1.0, 1.0], 1: [-1.0]},\n",
       "  (18, 3, True): {0: [-1.0, 1.0, 0.0, 1.0, 1.0, 1.0, 0.0], 1: []},\n",
       "  (6, 9, False): {0: [-1.0, 1.0, -1.0], 1: [-1.0, -1.0]},\n",
       "  (9, 9, False): {0: [-1.0, -1.0, -1.0, -1.0, -1.0, -1.0, 1.0, 1.0, 1.0],\n",
       "   1: [-1.0, -1.0]},\n",
       "  (12, 2, True): {0: [-1.0], 1: [-1.0]},\n",
       "  (5, 9, False): {0: [-1.0], 1: [-1.0, -1.0]},\n",
       "  (4, 4, False): {0: [-1.0, -1.0], 1: [-1.0]},\n",
       "  (12, 1, True): {0: [-1.0], 1: [1.0]},\n",
       "  (4, 9, False): {0: [1.0], 1: [1.0, -1.0]},\n",
       "  (18, 2, True): {0: [1.0, 1.0, -1.0], 1: [-1.0, 1.0, -1.0]},\n",
       "  (12, 3, True): {0: [-1.0], 1: []},\n",
       "  (18, 6, True): {0: [-1.0], 1: [-1.0, 1.0]},\n",
       "  (4, 7, False): {0: [-1.0, -1.0], 1: [-1.0]},\n",
       "  (5, 3, False): {0: [1.0], 1: [1.0, -1.0]},\n",
       "  (13, 2, True): {0: [1.0], 1: [-1.0]},\n",
       "  (5, 2, False): {0: [1.0, -1.0], 1: [1.0]},\n",
       "  (15, 6, True): {0: [-1.0], 1: []},\n",
       "  (14, 7, True): {0: [-1.0], 1: []},\n",
       "  (17, 5, True): {0: [1.0, -1.0, -1.0], 1: []}})"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q,rewards"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "26d5c8a7",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-10T01:41:07.670677Z",
     "start_time": "2024-05-10T01:41:07.664800Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1261.0"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "total_rewards=0\n",
    "for k,v in rewards.items():\n",
    "    total_rewards+=sum(v[0])\n",
    "    total_rewards+=sum(v[1])\n",
    "total_rewards"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "a79375bb",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-10T01:41:14.057631Z",
     "start_time": "2024-05-10T01:41:14.020597Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{(16, 10, False): [0.8, 0.2],\n",
       " (6, 7, False): [0.2, 0.8],\n",
       " (16, 7, False): [0.8, 0.2],\n",
       " (15, 7, False): [0.8, 0.2],\n",
       " (21, 7, False): [0.8, 0.2],\n",
       " (10, 8, False): [0.2, 0.8],\n",
       " (9, 8, False): [0.2, 0.8],\n",
       " (18, 8, False): [0.8, 0.2],\n",
       " (16, 4, False): [0.2, 0.8],\n",
       " (21, 4, False): [0.8, 0.2],\n",
       " (21, 9, True): [0.8, 0.2],\n",
       " (14, 7, False): [0.2, 0.8],\n",
       " (18, 7, False): [0.8, 0.2],\n",
       " (12, 10, False): [0.2, 0.8],\n",
       " (17, 10, False): [0.8, 0.2],\n",
       " (15, 6, False): [0.8, 0.2],\n",
       " (20, 9, False): [0.8, 0.2],\n",
       " (18, 10, False): [0.8, 0.2],\n",
       " (10, 2, False): [0.2, 0.8],\n",
       " (20, 2, False): [0.8, 0.2],\n",
       " (20, 10, False): [0.8, 0.2],\n",
       " (21, 10, False): [0.8, 0.2],\n",
       " (21, 6, True): [0.8, 0.2],\n",
       " (17, 4, True): [0.2, 0.8],\n",
       " (20, 7, False): [0.8, 0.2],\n",
       " (13, 1, False): [0.8, 0.2],\n",
       " (20, 1, False): [0.8, 0.2],\n",
       " (15, 5, True): [0.8, 0.2],\n",
       " (19, 10, False): [0.8, 0.2],\n",
       " (17, 5, False): [0.8, 0.2],\n",
       " (12, 2, False): [0.2, 0.8],\n",
       " (19, 2, False): [0.8, 0.2],\n",
       " (10, 1, False): [0.8, 0.2],\n",
       " (11, 6, False): [0.2, 0.8],\n",
       " (16, 6, False): [0.8, 0.2],\n",
       " (19, 6, False): [0.8, 0.2],\n",
       " (15, 10, False): [0.8, 0.2],\n",
       " (21, 10, True): [0.8, 0.2],\n",
       " (11, 7, False): [0.2, 0.8],\n",
       " (12, 4, False): [0.8, 0.2],\n",
       " (19, 5, False): [0.8, 0.2],\n",
       " (18, 2, False): [0.8, 0.2],\n",
       " (19, 5, True): [0.2, 0.8],\n",
       " (20, 6, False): [0.8, 0.2],\n",
       " (21, 8, True): [0.8, 0.2],\n",
       " (17, 1, False): [0.2, 0.8],\n",
       " (15, 8, True): [0.2, 0.8],\n",
       " (19, 4, True): [0.8, 0.2],\n",
       " (12, 1, False): [0.8, 0.2],\n",
       " (18, 1, True): [0.8, 0.2],\n",
       " (21, 1, True): [0.8, 0.2],\n",
       " (15, 1, False): [0.8, 0.2],\n",
       " (11, 10, False): [0.2, 0.8],\n",
       " (9, 10, False): [0.2, 0.8],\n",
       " (18, 9, False): [0.8, 0.2],\n",
       " (8, 10, False): [0.8, 0.2],\n",
       " (14, 2, False): [0.8, 0.2],\n",
       " (15, 1, True): [0.8, 0.2],\n",
       " (17, 1, True): [0.8, 0.2],\n",
       " (15, 10, True): [0.2, 0.8],\n",
       " (14, 10, False): [0.8, 0.2],\n",
       " (15, 8, False): [0.8, 0.2],\n",
       " (13, 3, False): [0.8, 0.2],\n",
       " (14, 9, False): [0.2, 0.8],\n",
       " (17, 4, False): [0.8, 0.2],\n",
       " (17, 9, True): [0.8, 0.2],\n",
       " (14, 10, True): [0.8, 0.2],\n",
       " (18, 10, True): [0.8, 0.2],\n",
       " (12, 9, False): [0.2, 0.8],\n",
       " (14, 6, False): [0.2, 0.8],\n",
       " (17, 8, False): [0.8, 0.2],\n",
       " (10, 6, False): [0.2, 0.8],\n",
       " (12, 6, False): [0.8, 0.2],\n",
       " (11, 8, False): [0.2, 0.8],\n",
       " (20, 8, False): [0.8, 0.2],\n",
       " (21, 2, True): [0.8, 0.2],\n",
       " (21, 2, False): [0.8, 0.2],\n",
       " (15, 9, False): [0.8, 0.2],\n",
       " (17, 9, False): [0.8, 0.2],\n",
       " (11, 2, False): [0.2, 0.8],\n",
       " (14, 4, True): [0.8, 0.2],\n",
       " (14, 4, False): [0.2, 0.8],\n",
       " (21, 3, True): [0.8, 0.2],\n",
       " (20, 3, False): [0.8, 0.2],\n",
       " (12, 5, True): [0.8, 0.2],\n",
       " (13, 10, False): [0.2, 0.8],\n",
       " (11, 1, False): [0.2, 0.8],\n",
       " (21, 1, False): [0.8, 0.2],\n",
       " (13, 4, True): [0.2, 0.8],\n",
       " (16, 4, True): [0.8, 0.2],\n",
       " (10, 4, False): [0.8, 0.2],\n",
       " (18, 3, False): [0.8, 0.2],\n",
       " (17, 2, True): [0.8, 0.2],\n",
       " (17, 6, False): [0.8, 0.2],\n",
       " (18, 6, False): [0.8, 0.2],\n",
       " (19, 4, False): [0.8, 0.2],\n",
       " (16, 8, False): [0.8, 0.2],\n",
       " (12, 3, False): [0.2, 0.8],\n",
       " (11, 3, False): [0.2, 0.8],\n",
       " (15, 3, False): [0.8, 0.2],\n",
       " (15, 9, True): [0.8, 0.2],\n",
       " (12, 6, True): [0.8, 0.2],\n",
       " (13, 4, False): [0.2, 0.8],\n",
       " (12, 8, False): [0.2, 0.8],\n",
       " (10, 3, False): [0.8, 0.2],\n",
       " (19, 7, False): [0.8, 0.2],\n",
       " (10, 7, False): [0.8, 0.2],\n",
       " (19, 9, True): [0.2, 0.8],\n",
       " (20, 9, True): [0.8, 0.2],\n",
       " (7, 9, False): [0.8, 0.2],\n",
       " (7, 4, False): [0.8, 0.2],\n",
       " (4, 1, False): [0.8, 0.2],\n",
       " (12, 7, True): [0.2, 0.8],\n",
       " (16, 5, False): [0.8, 0.2],\n",
       " (7, 1, False): [0.8, 0.2],\n",
       " (13, 10, True): [0.2, 0.8],\n",
       " (17, 8, True): [0.2, 0.8],\n",
       " (5, 6, False): [0.8, 0.2],\n",
       " (20, 4, False): [0.8, 0.2],\n",
       " (11, 4, False): [0.8, 0.2],\n",
       " (13, 2, False): [0.2, 0.8],\n",
       " (16, 1, True): [0.2, 0.8],\n",
       " (14, 1, False): [0.8, 0.2],\n",
       " (18, 1, False): [0.8, 0.2],\n",
       " (19, 8, False): [0.8, 0.2],\n",
       " (20, 4, True): [0.8, 0.2],\n",
       " (18, 4, False): [0.8, 0.2],\n",
       " (14, 3, False): [0.8, 0.2],\n",
       " (8, 9, False): [0.2, 0.8],\n",
       " (17, 7, False): [0.8, 0.2],\n",
       " (12, 5, False): [0.8, 0.2],\n",
       " (10, 10, False): [0.2, 0.8],\n",
       " (18, 8, True): [0.2, 0.8],\n",
       " (18, 5, False): [0.8, 0.2],\n",
       " (21, 5, False): [0.8, 0.2],\n",
       " (19, 7, True): [0.2, 0.8],\n",
       " (6, 10, False): [0.8, 0.2],\n",
       " (16, 3, False): [0.2, 0.8],\n",
       " (16, 2, False): [0.8, 0.2],\n",
       " (13, 8, False): [0.2, 0.8],\n",
       " (17, 10, True): [0.8, 0.2],\n",
       " (17, 2, False): [0.8, 0.2],\n",
       " (21, 5, True): [0.8, 0.2],\n",
       " (15, 2, False): [0.2, 0.8],\n",
       " (14, 5, False): [0.8, 0.2],\n",
       " (17, 6, True): [0.8, 0.2],\n",
       " (14, 8, False): [0.2, 0.8],\n",
       " (12, 7, False): [0.8, 0.2],\n",
       " (19, 1, False): [0.8, 0.2],\n",
       " (15, 7, True): [0.8, 0.2],\n",
       " (16, 7, True): [0.8, 0.2],\n",
       " (21, 7, True): [0.8, 0.2],\n",
       " (9, 3, False): [0.8, 0.2],\n",
       " (17, 3, False): [0.8, 0.2],\n",
       " (8, 2, False): [0.8, 0.2],\n",
       " (9, 4, False): [0.8, 0.2],\n",
       " (8, 6, False): [0.8, 0.2],\n",
       " (5, 10, False): [0.8, 0.2],\n",
       " (13, 9, False): [0.2, 0.8],\n",
       " (21, 3, False): [0.8, 0.2],\n",
       " (7, 10, False): [0.2, 0.8],\n",
       " (19, 3, False): [0.8, 0.2],\n",
       " (19, 9, False): [0.8, 0.2],\n",
       " (16, 9, False): [0.8, 0.2],\n",
       " (15, 4, False): [0.8, 0.2],\n",
       " (20, 5, True): [0.8, 0.2],\n",
       " (20, 6, True): [0.8, 0.2],\n",
       " (7, 5, False): [0.2, 0.8],\n",
       " (18, 5, True): [0.8, 0.2],\n",
       " (15, 4, True): [0.2, 0.8],\n",
       " (18, 9, True): [0.8, 0.2],\n",
       " (19, 10, True): [0.2, 0.8],\n",
       " (16, 1, False): [0.8, 0.2],\n",
       " (19, 2, True): [0.8, 0.2],\n",
       " (7, 2, False): [0.2, 0.8],\n",
       " (14, 8, True): [0.8, 0.2],\n",
       " (20, 5, False): [0.8, 0.2],\n",
       " (13, 8, True): [0.8, 0.2],\n",
       " (20, 10, True): [0.8, 0.2],\n",
       " (13, 7, False): [0.8, 0.2],\n",
       " (4, 5, False): [0.8, 0.2],\n",
       " (9, 5, False): [0.2, 0.8],\n",
       " (9, 6, False): [0.2, 0.8],\n",
       " (21, 9, False): [0.8, 0.2],\n",
       " (6, 2, False): [0.8, 0.2],\n",
       " (15, 5, False): [0.8, 0.2],\n",
       " (13, 6, False): [0.8, 0.2],\n",
       " (18, 7, True): [0.8, 0.2],\n",
       " (12, 9, True): [0.2, 0.8],\n",
       " (4, 8, False): [0.2, 0.8],\n",
       " (8, 5, False): [0.2, 0.8],\n",
       " (7, 7, False): [0.2, 0.8],\n",
       " (12, 10, True): [0.8, 0.2],\n",
       " (6, 1, False): [0.8, 0.2],\n",
       " (9, 1, False): [0.2, 0.8],\n",
       " (10, 5, False): [0.2, 0.8],\n",
       " (8, 1, False): [0.8, 0.2],\n",
       " (7, 8, False): [0.2, 0.8],\n",
       " (13, 5, False): [0.2, 0.8],\n",
       " (10, 9, False): [0.2, 0.8],\n",
       " (8, 8, False): [0.2, 0.8],\n",
       " (4, 10, False): [0.8, 0.2],\n",
       " (11, 5, False): [0.2, 0.8],\n",
       " (11, 9, False): [0.2, 0.8],\n",
       " (6, 3, False): [0.8, 0.2],\n",
       " (16, 6, True): [0.8, 0.2],\n",
       " (6, 4, False): [0.2, 0.8],\n",
       " (6, 6, False): [0.8, 0.2],\n",
       " (19, 6, True): [0.8, 0.2],\n",
       " (4, 6, False): [0.2, 0.8],\n",
       " (14, 3, True): [0.8, 0.2],\n",
       " (16, 10, True): [0.2, 0.8],\n",
       " (8, 7, False): [0.8, 0.2],\n",
       " (18, 4, True): [0.8, 0.2],\n",
       " (13, 1, True): [0.8, 0.2],\n",
       " (14, 1, True): [0.8, 0.2],\n",
       " (20, 1, True): [0.8, 0.2],\n",
       " (17, 3, True): [0.2, 0.8],\n",
       " (19, 3, True): [0.2, 0.8],\n",
       " (20, 3, True): [0.8, 0.2],\n",
       " (21, 4, True): [0.8, 0.2],\n",
       " (21, 6, False): [0.8, 0.2],\n",
       " (17, 7, True): [0.2, 0.8],\n",
       " (19, 1, True): [0.8, 0.2],\n",
       " (16, 2, True): [0.8, 0.2],\n",
       " (6, 5, False): [0.8, 0.2],\n",
       " (5, 1, False): [0.8, 0.2],\n",
       " (20, 7, True): [0.8, 0.2],\n",
       " (7, 6, False): [0.8, 0.2],\n",
       " (15, 3, True): [0.8, 0.2],\n",
       " (16, 3, True): [0.8, 0.2],\n",
       " (14, 2, True): [0.2, 0.8],\n",
       " (13, 9, True): [0.2, 0.8],\n",
       " (4, 3, False): [0.8, 0.2],\n",
       " (16, 8, True): [0.2, 0.8],\n",
       " (9, 7, False): [0.8, 0.2],\n",
       " (9, 2, False): [0.2, 0.8],\n",
       " (13, 6, True): [0.2, 0.8],\n",
       " (20, 2, True): [0.8, 0.2],\n",
       " (13, 5, True): [0.2, 0.8],\n",
       " (16, 5, True): [0.8, 0.2],\n",
       " (5, 7, False): [0.8, 0.2],\n",
       " (20, 8, True): [0.8, 0.2],\n",
       " (8, 4, False): [0.2, 0.8],\n",
       " (21, 8, False): [0.8, 0.2],\n",
       " (5, 4, False): [0.8, 0.2],\n",
       " (13, 7, True): [0.8, 0.2],\n",
       " (5, 8, False): [0.8, 0.2],\n",
       " (6, 8, False): [0.8, 0.2],\n",
       " (15, 2, True): [0.2, 0.8],\n",
       " (8, 3, False): [0.2, 0.8],\n",
       " (4, 2, False): [0.8, 0.2],\n",
       " (13, 3, True): [0.2, 0.8],\n",
       " (16, 9, True): [0.2, 0.8],\n",
       " (14, 9, True): [0.8, 0.2],\n",
       " (5, 5, False): [0.8, 0.2],\n",
       " (14, 5, True): [0.8, 0.2],\n",
       " (14, 6, True): [0.8, 0.2],\n",
       " (7, 3, False): [0.8, 0.2],\n",
       " (19, 8, True): [0.8, 0.2],\n",
       " (18, 3, True): [0.8, 0.2],\n",
       " (6, 9, False): [0.8, 0.2],\n",
       " (9, 9, False): [0.8, 0.2],\n",
       " (12, 2, True): [0.8, 0.2],\n",
       " (5, 9, False): [0.8, 0.2],\n",
       " (4, 4, False): [0.8, 0.2],\n",
       " (12, 1, True): [0.2, 0.8],\n",
       " (4, 9, False): [0.8, 0.2],\n",
       " (18, 2, True): [0.8, 0.2],\n",
       " (12, 3, True): [0.2, 0.8],\n",
       " (18, 6, True): [0.2, 0.8],\n",
       " (4, 7, False): [0.8, 0.2],\n",
       " (5, 3, False): [0.8, 0.2],\n",
       " (13, 2, True): [0.8, 0.2],\n",
       " (5, 2, False): [0.2, 0.8],\n",
       " (15, 6, True): [0.2, 0.8],\n",
       " (14, 7, True): [0.2, 0.8],\n",
       " (17, 5, True): [0.2, 0.8]}"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "policy"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "12e5c4de",
   "metadata": {},
   "source": [
    "## 时序差分方法"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "dc633f4f",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-10T01:43:17.828136Z",
     "start_time": "2024-05-10T01:43:17.821640Z"
    }
   },
   "outputs": [],
   "source": [
    "#模拟回合\n",
    "def generate_episodes(Q,policy):\n",
    "    #回合观测序列表\n",
    "    episode=[]\n",
    "    #初始化环境状态\n",
    "    state,_=env.reset()\n",
    "    while True:\n",
    "        #如果第一次出现,将他添加到Q和policy中\n",
    "        if state not in Q.keys():\n",
    "            Q[state]={0:0,1:0}#初始化stick与hit的Q值\n",
    "            policy[state]=[0.5,0.5] #初始化stick与hit的概率,各为0.5\n",
    "            rewards[state]={0:[],1:[]} #初始化空列表用于储存累积奖励\n",
    "        #利用policy采样一个动作\n",
    "        action=np.random.choice([0,1],p=policy[state],size=1)[0]\n",
    "        #与环境交互,产生奖励与下一状态\n",
    "        next_state,reward,terminated,truncated,info=env.step(action)\n",
    "        #将状态,动作,奖励添加到epsisode中\n",
    "        episode.append((state,action,reward,next_state))\n",
    "        if terminated:\n",
    "            break\n",
    "        #更新状态\n",
    "        state=next_state\n",
    "    return episode"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "00ec0dd9",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-10T01:45:46.396146Z",
     "start_time": "2024-05-10T01:45:45.260336Z"
    }
   },
   "outputs": [],
   "source": [
    "for i in range(num_episodes):\n",
    "    #产生一个观测序列\n",
    "    episode=generate_episodes(Q,policy)\n",
    "    #初始化累积奖励\n",
    "    episode_sum_reward=0.0\n",
    "    #反向遍历观测序列中的每一步\n",
    "    for t in range(len(episode))[::-1]:\n",
    "        state,action,reward,next_state=episode[t]\n",
    "        if next_state not in Q.keys():\n",
    "            Q[next_state]={0:0.0,1:0.0}\n",
    "        #计算累积奖励\n",
    "        episode_sum_reward+=reward\n",
    "        rewards[state][action].append(episode_sum_reward)\n",
    "        #更新Q表中的Q值\n",
    "        Q[state][action]+=alpha*(reward+max(Q[next_state].values())-Q[state][action])\n",
    "        #更新策略\n",
    "        policy_action=np.argmax(list(Q[state].values()))\n",
    "        policy[state][policy_action]=1-explore_rate\n",
    "        policy[state][1-policy_action]=explore_rate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "6d9ad588",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-10T01:45:58.567589Z",
     "start_time": "2024-05-10T01:45:58.515089Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{(14, 3, False): {0: -0.5539944595875549, 1: -0.4407004558899782},\n",
       " (18, 3, False): {0: 0.30000000000000004, 1: -0.34390000000000004},\n",
       " (8, 5, False): {0: -0.1, 1: -0.04126621430313648},\n",
       " (18, 5, False): {0: 0.5, 1: -0.5695327900000001},\n",
       " (18, 10, False): {0: -0.7083770443178603, 1: 0.023929874113274796},\n",
       " (11, 10, False): {0: 1.320083221589547, 1: 4.00318710860462},\n",
       " (16, 1, False): {0: -1.0307343408840353, 1: -0.7320960036725904},\n",
       " (20, 10, True): {0: 1.4, 1: -0.05467482539840299},\n",
       " (15, 5, False): {0: -0.5488784742852214, 1: -0.4027860994033855},\n",
       " (15, 9, False): {0: -0.7459407900506331, 1: 0.19525053057010955},\n",
       " (16, 8, False): {0: -0.7014884737946615, 1: 0.15693713087527292},\n",
       " (19, 3, False): {0: 1.6, 1: -0.46855900000000006},\n",
       " (10, 7, False): {0: 0.06755717829866614, 1: 0.6402039400350797},\n",
       " (6, 10, False): {0: -0.5347809111070319, 1: 0.3268644864443065},\n",
       " (21, 10, True): {0: 5.899999999999995, 1: 2.7503049813893443},\n",
       " (14, 10, False): {0: -0.13657202783193048, 1: 0.019641790961124735},\n",
       " (14, 9, False): {0: -0.5905131973221861, 1: 0.19152058121032733},\n",
       " (18, 2, False): {0: -0.29780202270053513, 1: -0.5771963838743344},\n",
       " (20, 2, False): {0: 3.600000000000002, 1: -0.58123207545039},\n",
       " (16, 10, False): {0: -0.6394964598873705, 1: 1.4192285918373453},\n",
       " (24, 10, False): {0: 0.0, 1: 0.0},\n",
       " (19, 10, False): {0: -0.26743323986889256, 1: -0.20871053705800618},\n",
       " (25, 10, False): {0: 0.0, 1: 0.0},\n",
       " (21, 5, True): {0: 1.103719, 1: 0.14442899201},\n",
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       " (19, 5, True): {0: 0.20000000000000004, 1: 0},\n",
       " (5, 9, False): {0: 0, 1: 0.0008574116008380401},\n",
       " (31, 1, False): {0: 0.0, 1: 0.0},\n",
       " (6, 3, False): {0: 0.2, 1: -0.03250250520097381},\n",
       " (31, 6, False): {0: 0.0, 1: 0.0},\n",
       " (17, 3, True): {0: -0.19, 1: 0},\n",
       " (12, 8, True): {0: -0.1, 1: -0.02424425284512628},\n",
       " (16, 2, True): {0: -0.1, 1: -0.0047755386747562805},\n",
       " (4, 2, False): {0: -0.1, 1: 0.12414403228270694}}"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "e76c4f31",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-10T01:46:03.437165Z",
     "start_time": "2024-05-10T01:46:03.405734Z"
    }
   },
   "outputs": [
    {
     "data": {
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       " (9, 3, False): [0.2, 0.8],\n",
       " (13, 9, True): [0.2, 0.8],\n",
       " (17, 2, True): [0.2, 0.8],\n",
       " (7, 8, False): [0.2, 0.8],\n",
       " (18, 10, True): [0.2, 0.8],\n",
       " (21, 4, True): [0.8, 0.2],\n",
       " (16, 4, True): [0.2, 0.8],\n",
       " (19, 6, True): [0.8, 0.2],\n",
       " (16, 6, True): [0.2, 0.8],\n",
       " (15, 2, True): [0.2, 0.8],\n",
       " (13, 8, True): [0.2, 0.8],\n",
       " (18, 8, True): [0.8, 0.2],\n",
       " (14, 8, True): [0.2, 0.8],\n",
       " (13, 7, True): [0.2, 0.8],\n",
       " (20, 7, True): [0.2, 0.8],\n",
       " (5, 3, False): [0.8, 0.2],\n",
       " (14, 2, True): [0.2, 0.8],\n",
       " (19, 2, True): [0.8, 0.2],\n",
       " (5, 1, False): [0.2, 0.8],\n",
       " (5, 4, False): [0.8, 0.2],\n",
       " (8, 7, False): [0.8, 0.2],\n",
       " (15, 6, True): [0.2, 0.8],\n",
       " (13, 5, True): [0.8, 0.2],\n",
       " (9, 7, False): [0.2, 0.8],\n",
       " (21, 7, False): [0.8, 0.2],\n",
       " (19, 3, True): [0.8, 0.2],\n",
       " (12, 9, True): [0.2, 0.8],\n",
       " (20, 2, True): [0.2, 0.8],\n",
       " (6, 2, False): [0.2, 0.8],\n",
       " (15, 3, True): [0.8, 0.2],\n",
       " (12, 2, True): [0.2, 0.8],\n",
       " (9, 8, False): [0.2, 0.8],\n",
       " (5, 2, False): [0.2, 0.8],\n",
       " (4, 8, False): [0.2, 0.8],\n",
       " (16, 10, True): [0.2, 0.8],\n",
       " (12, 6, True): [0.2, 0.8],\n",
       " (14, 3, True): [0.8, 0.2],\n",
       " (15, 9, True): [0.2, 0.8],\n",
       " (6, 9, False): [0.2, 0.8],\n",
       " (16, 5, True): [0.2, 0.8],\n",
       " (21, 6, False): [0.8, 0.2],\n",
       " (13, 6, True): [0.8, 0.2],\n",
       " (17, 4, True): [0.8, 0.2],\n",
       " (17, 1, True): [0.2, 0.8],\n",
       " (20, 3, True): [0.8, 0.2],\n",
       " (12, 3, True): [0.2, 0.8],\n",
       " (13, 3, True): [0.2, 0.8],\n",
       " (12, 5, True): [0.8, 0.2],\n",
       " (6, 1, False): [0.8, 0.2],\n",
       " (16, 7, True): [0.8, 0.2],\n",
       " (20, 8, True): [0.8, 0.2],\n",
       " (7, 2, False): [0.2, 0.8],\n",
       " (4, 4, False): [0.2, 0.8],\n",
       " (12, 7, True): [0.2, 0.8],\n",
       " (4, 9, False): [0.2, 0.8],\n",
       " (4, 3, False): [0.2, 0.8],\n",
       " (16, 1, True): [0.2, 0.8],\n",
       " (5, 6, False): [0.2, 0.8],\n",
       " (17, 7, True): [0.2, 0.8],\n",
       " (4, 5, False): [0.2, 0.8],\n",
       " (15, 8, True): [0.2, 0.8],\n",
       " (4, 1, False): [0.2, 0.8],\n",
       " (15, 7, True): [0.2, 0.8],\n",
       " (14, 1, True): [0.8, 0.2],\n",
       " (19, 5, True): [0.8, 0.2],\n",
       " (5, 9, False): [0.2, 0.8],\n",
       " (6, 3, False): [0.8, 0.2],\n",
       " (17, 3, True): [0.2, 0.8],\n",
       " (12, 8, True): [0.2, 0.8],\n",
       " (16, 2, True): [0.2, 0.8],\n",
       " (4, 2, False): [0.2, 0.8]}"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "policy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "bcee3c0f",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-10T01:46:30.519941Z",
     "start_time": "2024-05-10T01:46:30.511891Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1659.0"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "total_rewards=0\n",
    "for k,v in rewards.items():\n",
    "    total_rewards+=sum(v[0])\n",
    "    total_rewards+=sum(v[1])\n",
    "total_rewards"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "394e1b79",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-10T02:00:49.922975Z",
     "start_time": "2024-05-10T02:00:49.918986Z"
    }
   },
   "outputs": [],
   "source": [
    "import time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "927fea26",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-10T02:01:15.608577Z",
     "start_time": "2024-05-10T02:01:15.584493Z"
    }
   },
   "outputs": [
    {
     "ename": "error",
     "evalue": "font not initialized",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31merror\u001b[0m                                     Traceback (most recent call last)",
      "\u001b[1;32m~\\AppData\\Local\\Temp\\ipykernel_4224\\2300459922.py\u001b[0m in \u001b[0;36m<cell line: 2>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[0mobservation\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0m_\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0menv\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mreset\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 2\u001b[1;33m \u001b[0mgym_helper\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mGymHelper\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0menv\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      3\u001b[0m \u001b[1;31m#进去十步游戏\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      4\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m10\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      5\u001b[0m     \u001b[1;31m#title为当前步数数\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\AppData\\Local\\Temp\\ipykernel_4224\\1653382563.py\u001b[0m in \u001b[0;36m__init__\u001b[1;34m(self, env, figsize)\u001b[0m\n\u001b[0;32m      4\u001b[0m         \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfigsize\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mfigsize\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      5\u001b[0m         \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfigure\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mfigsize\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mfigsize\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 6\u001b[1;33m         \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mimg\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mimshow\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0menv\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mrender\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      7\u001b[0m     \u001b[1;32mdef\u001b[0m \u001b[0mrender\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mtitle\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;32mNone\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      8\u001b[0m         \u001b[0mimg_data\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0menv\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mrender\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mI:\\AI\\Anaconda\\lib\\site-packages\\gym\\wrappers\\order_enforcing.py\u001b[0m in \u001b[0;36mrender\u001b[1;34m(self, *args, **kwargs)\u001b[0m\n\u001b[0;32m     49\u001b[0m                 \u001b[1;34m\"set `disable_render_order_enforcing=True` on the OrderEnforcer wrapper.\"\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     50\u001b[0m             )\n\u001b[1;32m---> 51\u001b[1;33m         \u001b[1;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0menv\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mrender\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     52\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     53\u001b[0m     \u001b[1;33m@\u001b[0m\u001b[0mproperty\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mI:\\AI\\Anaconda\\lib\\site-packages\\gym\\wrappers\\env_checker.py\u001b[0m in \u001b[0;36mrender\u001b[1;34m(self, *args, **kwargs)\u001b[0m\n\u001b[0;32m     53\u001b[0m             \u001b[1;32mreturn\u001b[0m \u001b[0menv_render_passive_checker\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0menv\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     54\u001b[0m         \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 55\u001b[1;33m             \u001b[1;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0menv\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mrender\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;32mI:\\AI\\Anaconda\\lib\\site-packages\\gym\\envs\\toy_text\\blackjack.py\u001b[0m in \u001b[0;36mrender\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m    231\u001b[0m             \u001b[1;32mreturn\u001b[0m \u001b[0mfont\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    232\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 233\u001b[1;33m         small_font = get_font(\n\u001b[0m\u001b[0;32m    234\u001b[0m             \u001b[0mos\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mpath\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mjoin\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"font\"\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m\"Minecraft.ttf\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mscreen_height\u001b[0m \u001b[1;33m//\u001b[0m \u001b[1;36m15\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    235\u001b[0m         )\n",
      "\u001b[1;32mI:\\AI\\Anaconda\\lib\\site-packages\\gym\\envs\\toy_text\\blackjack.py\u001b[0m in \u001b[0;36mget_font\u001b[1;34m(path, size)\u001b[0m\n\u001b[0;32m    228\u001b[0m         \u001b[1;32mdef\u001b[0m \u001b[0mget_font\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mpath\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0msize\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    229\u001b[0m             \u001b[0mcwd\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mos\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mpath\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdirname\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0m__file__\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 230\u001b[1;33m             \u001b[0mfont\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mpygame\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfont\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mFont\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mos\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mpath\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mjoin\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mcwd\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mpath\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0msize\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    231\u001b[0m             \u001b[1;32mreturn\u001b[0m \u001b[0mfont\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    232\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31merror\u001b[0m: font not initialized"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 300x300 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "observation,_=env.reset()\n",
    "gym_helper=GymHelper(env)\n",
    "#进去十步游戏\n",
    "for i in range(10):\n",
    "    #title为当前步数数\n",
    "    gym_helper.render(title=str(i))\n",
    "    #通过已经求得的最优策略,找到当前状态的最优动作\n",
    "    action=np.argmax(policy[observation])\n",
    "    observation,reward,terminated,truncated,info=env.step(action)\n",
    "    time.sleep(0.5)\n",
    "    if terminated or truncated:\n",
    "        break\n",
    "gym_helper.render(title=\"Finished\")\n",
    "env.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3755a431",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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